# Multiply 2-Digit Numbers With Area Models ## Section A: Multiple Choice Questions
Q1: What is the area model also known as when multiplying numbers? (a) The box method (b) The circle method (c) The line method (d) The dot method
Solution:
Ans: (a) Explanation: The area model is also called the box method because we draw a rectangle or box and divide it into parts to multiply.
Q2: In an area model for \(24 \times 13\), if you break 24 into 20 + 4 and 13 into 10 + 3, how many smaller rectangles will you have? (a) 2 (b) 3 (c) 4 (d) 5
Solution:
Ans: (c) Explanation: When you break both numbers into two parts each, you create \(2 \times 2 = 4\) smaller rectangles in the area model.
Q3: Using the area model, what is \(20 \times 10\)? (a) 30 (b) 200 (c) 2,000 (d) 210
Solution:
Ans: (b) Explanation: When multiplying \(20 \times 10\), we get \(200\). This represents one section of an area model when multiplying two 2-digit numbers.
Q4: What is \(15 \times 12\) using the area model with 15 broken into 10 + 5 and 12 broken into 10 + 2? (a) 150 (b) 170 (c) 180 (d) 160
Solution:
Ans: (c) Explanation: Using the area model: \(10 \times 10 = 100\) \(10 \times 2 = 20\) \(5 \times 10 = 50\) \(5 \times 2 = 10\) Add all parts: \(100 + 20 + 50 + 10 = 180\)
Q5: If one section of an area model shows \(30 \times 4 = 120\), which expression could this be part of? (a) \(34 \times 10\) (b) \(30 \times 14\) (c) \(34 \times 4\) (d) \(30 \times 40\)
Solution:
Ans: (b) Explanation: The section \(30 \times 4 = 120\) shows 30 being multiplied by 4. This would be part of \(30 \times 14\) where 14 is broken into 10 + 4, and one section is \(30 \times 4\).
Q6: What is the product of \(22 \times 11\) using an area model? (a) 232 (b) 242 (c) 252 (d) 222
Q7: In the area model for \(18 \times 25\), if you find \(10 \times 20 = 200\), what are the other three partial products? (a) \(10 \times 5\), \(8 \times 20\), \(8 \times 5\) (b) \(10 \times 5\), \(8 \times 25\), \(18 \times 5\) (c) \(18 \times 5\), \(10 \times 25\), \(8 \times 20\) (d) \(20 \times 5\), \(8 \times 10\), \(8 \times 5\)
Solution:
Ans: (a) Explanation: Breaking 18 into \(10 + 8\) and 25 into \(20 + 5\), the four partial products are: \(10 \times 20 = 200\) \(10 \times 5 = 50\) \(8 \times 20 = 160\) \(8 \times 5 = 40\)
Q8: Which pair of numbers would NOT create exactly four sections in a standard area model? (a) 23 and 14 (b) 30 and 12 (c) 17 and 19 (d) 100 and 25
Solution:
Ans: (d) Explanation: When we break 100 into parts, we could use \(100 + 0\), which means one part is zero. This creates only two sections instead of four. The other pairs break naturally into two non-zero parts each, creating four sections.
## Section B: Fill in the Blanks Q9: The area model uses the concept of __________ to multiply two-digit numbers by breaking them into smaller parts.
Solution:
Ans: partial products Explanation: The area model breaks numbers into parts and multiplies each part separately to find partial products, which are then added together.
Q10: When using the area model to multiply \(32 \times 14\), if 32 is split into 30 and 2, then 14 should be split into __________ and __________.
Solution:
Ans: 10 and 4 Explanation: To use the area model, we break each number by place value. The number 14 breaks into 10 (the tens) and 4 (the ones).
Q11: In an area model, if one rectangular section has dimensions \(20 \times 30\), the area of that section is __________.
Solution:
Ans: 600 Explanation: The area of a rectangle is length times width. So \(20 \times 30 = 600\).
Q12: To find the final product in an area model, you must __________ all the partial products together.
Solution:
Ans: add Explanation: After finding all the partial products in each section of the area model, we add them to get the final answer.
Q13: If \(40 \times 20 = 800\) and \(40 \times 3 = 120\), then \(40 \times 23 = __________\).
Solution:
Ans: 920 Explanation: Using the distributive property, we add the partial products: \(800 + 120 = 920\).
Q14: The area model is especially helpful because it shows how multiplication relates to __________ and breaking numbers apart.
Solution:
Ans: area (or geometry) Explanation: The area model connects multiplication to finding the area of rectangles, making it a visual and geometric approach.
## Section C: Word Problems Q15: A rectangular garden is 18 feet long and 14 feet wide. Use the area model to find the total area of the garden. Show your work by breaking the numbers into tens and ones.
Solution:
Ans: Break 18 into \(10 + 8\) and 14 into \(10 + 4\): \(10 \times 10 = 100\) \(10 \times 4 = 40\) \(8 \times 10 = 80\) \(8 \times 4 = 32\) Add all parts: \(100 + 40 + 80 + 32 = 252\) Final Answer: 252 square feet
Q16: A bakery makes 23 trays of cookies each day. Each tray holds 15 cookies. Using the area model, how many cookies does the bakery make in one day?
Solution:
Ans: Break 23 into \(20 + 3\) and 15 into \(10 + 5\): \(20 \times 10 = 200\) \(20 \times 5 = 100\) \(3 \times 10 = 30\) \(3 \times 5 = 15\) Add all parts: \(200 + 100 + 30 + 15 = 345\) Final Answer: 345 cookies
Q17: A school auditorium has 27 rows of seats. Each row has 16 seats. Use the area model to calculate the total number of seats in the auditorium.
Solution:
Ans: Break 27 into \(20 + 7\) and 16 into \(10 + 6\): \(20 \times 10 = 200\) \(20 \times 6 = 120\) \(7 \times 10 = 70\) \(7 \times 6 = 42\) Add all parts: \(200 + 120 + 70 + 42 = 432\) Final Answer: 432 seats
Q18: A farmer plants apple trees in a rectangular pattern with 19 rows and 22 trees in each row. Using the area model, find the total number of apple trees.
Solution:
Ans: Break 19 into \(10 + 9\) and 22 into \(20 + 2\): \(10 \times 20 = 200\) \(10 \times 2 = 20\) \(9 \times 20 = 180\) \(9 \times 2 = 18\) Add all parts: \(200 + 20 + 180 + 18 = 418\) Final Answer: 418 apple trees
Q19: A toy store orders building blocks in boxes. Each box contains 24 bags, and each bag has 13 blocks. Use the area model to find the total number of blocks in one box.
Solution:
Ans: Break 24 into \(20 + 4\) and 13 into \(10 + 3\): \(20 \times 10 = 200\) \(20 \times 3 = 60\) \(4 \times 10 = 40\) \(4 \times 3 = 12\) Add all parts: \(200 + 60 + 40 + 12 = 312\) Final Answer: 312 blocks
Q20: A classroom floor is being covered with square tiles. The floor measures 35 feet by 12 feet. Using the area model, calculate how many square feet of tiles are needed.
Solution:
Ans: Break 35 into \(30 + 5\) and 12 into \(10 + 2\): \(30 \times 10 = 300\) \(30 \times 2 = 60\) \(5 \times 10 = 50\) \(5 \times 2 = 10\) Add all parts: \(300 + 60 + 50 + 10 = 420\) Final Answer: 420 square feet
The document Worksheet (with Solutions): Multiply 2-Digit Numbers With Area Models is a part of the Grade 4 Course Math Grade 4.
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